Missing faces on model
As far as I can see in the attached image, looks like you are doing the extrude using Vertex as the sub-object in edit mode, there's nothing wrong with that, except that you need to select all the vertices that are shaping the face before extruding. Alternatively, try using Faces instead as the selection method, by pressing Ctrl  + Tab while in edit mode, then choose Faces. The weird colored faces are simply faces with flipped normals, to unify the faces normals, select all faces, then press Ctrl  + N